Right to Roam campaigner Amy-Jane Beer said ancient sites needed to be accessible as they “connect us with our past and enrich our experience of the countryside”.
The group is calling for a change in the law to bring England in line with Scotland where, since 2003, there has existed a right of responsible access to most land.
Matthew Shaw, of the Stone Club, added: “Sites which are visited often have active groups caring for them – maintaining access, ensuring the stones are well looked after and liaising with the landowner.”
A spokeswoman for the Department for Culture, Media and Sport (DCMS) said the purpose of scheduling monuments was to preserve them for future generations and does not create new rights of public access.
A Historic England spokesman added that it did not require landowners to open their sites to the public.
“While not all are publicly accessible, we can also celebrate a site’s history through capturing and sharing information about it,” he added.